To understand language, humans must encode information from rapid, sequential streams of syllables--tracking their order and organizing them into words, phrases, and sentences. We used Near-Infrared Spectroscopy (NIRS) to determine whether human neonates are born with the capacity to track the positions of syllables in multisyllabic sequences. After familiarization with a six-syllable sequence, the neonate brain responded to the change (as shown by an increase in oxy-hemoglobin) when the two edge syllables switched positions but not when two middle syllables switched positions (Experiment 1), indicating that they encoded the syllables at the edges of sequences better than those in the middle. Moreover, when a 25 ms pause was inserted between the middle syllables as a segmentation cue, neonates' brains were sensitive to the change (Experiment 2), indicating that subtle cues in speech can signal a boundary, with enhanced encoding of the syllables located at the edges of that boundary. These findings suggest that neonates' brains can encode information from multisyllabic sequences and that this encoding is constrained. Moreover, subtle segmentation cues in a sequence of syllables provide a mechanism with which to accurately encode positional information from longer sequences. Tracking the order of syllables is necessary to understand language and our results suggest that the foundations for this encoding are present at birth.